摘要
本文对格的凸子格格进行了研究,给出了凸子格的两种定义,同时证明了这两个定义的等价性,得到了凸子格格是分配格、幂集格的充分必要条件,研究了凸子格格对格的刻画问题和凸子格的数量问题.
This paper studies the convex sub-lattice of lattice.Two definitions of convex sub-lattice are given and their equivalence is proved.The sufficient and necessary conditions for distributive lattice and power set lattice is the convex sub-lattice of lattice.The characterization of the convex sub-lattice of lattice to the original lattice and the number of the convex sub-lattices are studied.
引文
[1] Koh,K.M.,On the lattice of convex sub-lattices of a lattice[J].Nanta Math,1972,(6):18~37.
[2] Gratzer G.,General lattice theory[M].Academic Press,N.Y,1978.
[3] 侯耀平,关于格的凸子格格[J].科学通报,1999,38(17):1548~1550.
[4] Birkhoff G.,Lattice Theory[M].Third edition.Amer.Math.Soc.Providence.R.I,1967.
[5] S.Lavanya.,A new approach to the lattice of convex sub-lattices of a lattice[J].Algebra Universalis,1996,(35):63~71.
[6] 薛英.幂格与模糊幂格的性质[D].呼和浩特:内蒙古工业大学,2016.
[7] 黎爱平.分配格上的全序幂格[J].模糊系统与数学,2013,27(1):9~11.
[8] 黎爱平,双鹂.格的凸子格格与幂格[J].模糊系统与数学,2012,26(1):48~51.
[9] 黎爱平.相对凸子格与幂格[J].模糊系统与数学,2011,25(1):45~47.